Hi Jip,
The easiest way is to upgrade your current Joomla installation from version 3 to version 4. This way all your files and database data will remain unchanged.
If you need to perform a clean installation for Joomla 4 then you just need to copy the database tables and the uploaded images:
1. Install Showtime Image Gallery to the new Joomla 4 installation.
2. Export #__showtime_galleries and #__showtime_images from your current Joomla 3 installation and import them to the new Joomla 4 database.
3. Copy folder /media/showtime/storage from the current Joomla 3 installation to the new Joomla 4 installation.
At this point all your the galleries should be available in the new installation. Of course you will need to also migrate the data for the components that use those galleries.
For example any custom fields or articles that contain those galleries.
Regards